Multivariate techniques useful in the analysis of mental health data are developed at the theoretical level, and computer programs are written to implement these techniques. Four types of internal consistency coefficients are developed: a coefficient based on maximally predictable latent scores; a lower-bound coefficient that is invariant with respect to any rescaling of the variables; a class of rank-one coefficients; and a class of coefficients invariant with respect to the origin of the variables. Four types of exploratory factor analytic or component models are developed: scale-free, rank- free legitimate models; models that are invariant under translation of origin and change of scale; monotonic models that are invariant under monotonic transformtions of variables; and factor-score scale-free models. Three types of confirmatory factor analytic models are developed: rank-specified models producing legitimate solutions; loading-specified models; and multitrait-multimethod models. An oblique factor-score scale free transformation procedure is obtained. Related methods are also developed where possible. The main purpose of these various methods is to provide a technology that is useful in situations where traditional techniques are not appropriate or adequate.